Plz help me to solve
In how many years will the money deposited in a bank double itself,if the rate of intrest 12 1/2% per annum?
if compound interest,
(1+.125)^x = 2
x = 5.88 years
6 years to obtain the interest.
Bt its ans is 8year
To find the number of years it takes for the money to double, you can use the concept of compound interest.
The formula for compound interest is:
A = P(1 + r/n)^(nt)
Where:
A = total amount after interest
P = principal amount (initial deposit)
r = annual interest rate (in decimal form)
n = number of times interest is compounded per year
t = time in years
In this case, let's assume you deposit an amount P in the bank. The interest rate is 12 1/2% per annum, which can be written as 0.125 (since 12 1/2% = 12.5/100 = 0.125).
Since you want the money to double, the total amount A will be 2 times the principal amount (P).
Therefore, the formula becomes:
2P = P(1 + 0.125/n)^(nt)
Now, let's simplify the equation:
2 = (1 + 0.125/n)^(nt)
To solve for t, the number of years it takes for the money to double itself, you need to use logarithms to isolate t. Taking the natural logarithm (ln) of both sides of the equation, we get:
ln(2) = nt ln(1 + 0.125/n)
Now, divide both sides of the equation by n ln(1 + 0.125/n):
t = ln(2) / (n ln(1 + 0.125/n))
Keep in mind that the value of n is not given in the question. The compounding frequency can vary, such as annually (n = 1), semi-annually (n = 2), quarterly (n = 4), or monthly (n = 12). The choice of n depends on how often the interest is compounded.
Plug in the appropriate value of n into the above formula, calculate and round-off to the nearest whole number to determine the number of years it takes for the money to double.